Efficient Wasserstein barycenter in MATLAB
Author's updated version at https://github.com/bobye/WBC_Matlab
This package includes the propotype codes for computing the Wasserstein barycenter. The codes are released to reproduce parts of the experiments reported in the following journal paper:
- Jianbo Ye, Panruo Wu, James Z. Wang and Jia Li, "Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support", IEEE Transactions on Signal Processing, 2017 (arXiv:1510.00012 [stat.CO], September 2015), to appear.
A more efficient and scalable implementation in MPI and C is available.
The codes also implements algorithms in the following papers:
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré, "Iterative Bregman projections for regularized transportation problems." SIAM Journal on Scientific Computing 37.2 (2015): A1111-A1138.
Jianbo Ye and Jia Li, "Scaling Up Discrete Distribution Clustering Using ADMM", IEEE International Conference on Image Processing, Paris, France, October 2014.
Marco Cuturi and Arnaud Doucet. "Fast Computation of Wasserstein Barycenters.", International Conference on Machine Learning, Atlanta, USA, June 2013.
Jia Li and James Z. Wang. "Real-time computerized annotation of pictures." IEEE Transactions on Pattern Analysis and Machine Intelligence 30.6 (2008): 985-1002.
matlab contains prototype version in Matlab R2015b.
profile_centroid.m--- profiling the convergence of centroid updates
Wasserstein_Barycenter.m--- main function
profile_kantorovich.m--- profiling LP solution of transportation problem
centroid_sph*.m--- computing centroid of a single phase
The code is tested in Matlab 2015a
Try to run
profile_centroid.m from the project directory. Checkout the data structure used in the example.
This code also can be tailored to work with histogram data, but the coordinates of bins should also be supplied as support points in the data structure. Meanwhile, set the option for fixing the support points of WBC:
%% comment out this line to use fixed support points of barycenter options.support_points= 'fixed';
- How BADMM works for MNIST dataset? I was able to generate BADMM barycenter from 100 MNIST images (sparse representation). At Intel i7 3.4GHz PC, the pre-converged results at 200 seconds and 1000 seconds are depicted as follows respectively:
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Any publication of results obtained with the software must acknowledge its use by an appropriate citation to the article titled "Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support" published in the IEEE Transactions on Signal Processing in 2017.
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Author: Jianbo Ye, College of Information Sciences and Technology, firstname.lastname@example.org